If you want great circle distance, and are happy to think of the earth as a sphere, then it should just be arccos(dot(v,w)) where v,w are 3-vectors like v=[sin(lat), cos(lat)*sin(long), cos(lat)*cos(long)]… up to units. But perhaps a package called Geodesy will already have this somewhere?

Now that I look at the readme, it sounds like “distance” is probably a straight-line distance in 3D. Is this what you want?

They say "Future work may focus on geodesics and related calculations " which is what I was aiming for. But the package is more sophisticated than assuming the world is a sphere, and thus working out the accurate great-circle distance (i.e. geodesic length) accurately would be harder work.

To get the cartesian (2d-) distance on a map, have a look at Proj4.jl which is a Julia wrapper around a relatively widely used C library. As @improbable22 already wrote, this depends on the map projection.